Question: Express this product in scientific notation: $(5.80\times 10^{1})\times (8.00\times 10^{3})$
Explanation: Start by collecting like terms together. $= (5.80\times 8.00) \times (10^{1}\times 10^{3})$ When multiplying exponents with the same base, add the powers together. $= 46.4 \times 10^{1\,+\,3}$ $= 46.4 \times 10^{4}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the left without changing the value of our answer. $ $ We can use the fact that $46.4$ is the same as $4.640 \times 10$ $ = {4.640 \times 10} \times 10^{4} $ $= 4.640\times 10^{5}$